Flashcard - Proportional vs Non-Proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio. This means that as one quantity increases or decreases, the other does so in a consistent manner, represented by the equation y = kx, where k is a constant.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. This can be represented by equations that include a constant term or do not maintain a consistent ratio.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship on a graph is represented by a straight line that passes through the origin (0,0). If the line does not pass through the origin, it is non-proportional.

Front

How can you identify a non-proportional relationship from a table?

Back

In a table, a non-proportional relationship will show that the ratios of corresponding values are not constant. If the ratio changes as you move down the table, it is non-proportional.

Front

What does the equation y = kx represent?

Back

The equation y = kx represents a proportional relationship, where k is a constant that defines the ratio between y and x.

Front

What does the equation y = mx + b represent?

Back

The equation y = mx + b represents a linear relationship, where m is the slope and b is the y-intercept. If b is not zero, the relationship is non-proportional.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the graph crosses the y-axis. In a proportional relationship, the y-intercept is always zero.

Front

If a table shows the values (2, 4), (4, 8), (6, 12), what type of relationship does it indicate?

Back

This table indicates a proportional relationship because the ratio of y to x is constant (y/x = 2 for all pairs).

Front

If a graph shows a line that does not pass through the origin, what can you conclude?

Back

If a graph shows a line that does not pass through the origin, it indicates a non-proportional relationship.

Front

What is an example of a proportional relationship in real life?

Back

An example of a proportional relationship is the relationship between distance and time when traveling at a constant speed.